The young star of Come Look at the Baby does a spot of flyering on the fringe.
Photograph: Murdo Macleod for the Guardian

I love introducing people to the Edinburgh fringe. Even those who are not regular theatregoers are seduced by the excitement, the sense of possibility, the ease with which you can stroll up and buy a ticket for a show you fancy. It’s the most relaxed form of theatre-going, devoid of so many of the conventions that make people think theatre is not for them.

When my children were growing up, the fringe became a place where they spread their wings, taking their first steps towards independence and finding their own way about the city, discovering theatre and comedy for themselves and developing their own tastes. On the other hand, my father was 87 when he paid his first visit to the fringe, and he loved it too.

This year I introduced my grandson Hector to the festival. Hector is eight months old and, judging by his enthusiasm, I reckon it’s quite possible he will grow up to be a fringe regular. When he is a veteran festivalgoer, he will be able to reminisce about the afternoon he spent in the Traverse bar in 2016. Or maybe not.

There is a wonderful moment in The View from Castle Rock, staged by Stellar Quines at St Mark’s artSpace, when the Laidlaw family are boarding a ship. A cow and a pig are hoisted on a crane above their heads on the ship and Mary, who is holding baby James, thinks: “Someday he may remember this. I saw a cow and a pig fly through the air.Then he may wonder if it was a dream. And nobody will be there to tell him that it was not, that it happened on this ship.”

I thought about that as I took Hector around the fringe and we saw balloon sheep floating in the air in Head in the Clouds at the Royal Botanic Gardens, enjoyed the dreamy musical delights of Starcatchers’ Hup (Pleasance at Edinburgh International Conference Centre), in which he interacted with a person dressed as a racoon – just normal behaviour as far as Hector is concerned – and had his first experience of dance theatre with Barrowland Ballet’s excellent Poggle at Dance Space, a show whose rumbustious energy defies the idea that everything for babies has to be gentle.

As Anna Newell of Replay Theatre Company has observed, those who think that theatre for babies is a waste of time, because the child will not remember anything about it, are failing to take into account research showing that the first three years are fundamental to shaping who we are. So these shows should “be filled with experiences that are beautiful, challenging, imaginative, soothing, musical, creative, exciting and calming”. The three shows that Hector and I saw together were all those things and more.

There has been a steep rise in the number of shows for children on the fringe, although not all of them are entirely truthful about their suitability for particular age ranges. The needs of a three-year-old in a theatre are entirely different from those of a five-year-old.

I wasn’t surprised by the number of shows aimed directly at babies. When it comes to work for older children, we may not be as brave as companies such as Bronks from Belguim whose Us/Them at Summerhall demonstrates the kind of work that can be made for family audiences if you hold your nerve. But the UK has always been a forerunner in theatre for the very early years, with companies such as Oily Cart, Replay and Theatr Iolo leading the way.

I was delighted by the range and quality of shows for babies at the fringe. The exquisitely put together Hup and the energetic Poggle, in particular, were up there with the very best shows I saw, and perhaps tellingly, they were both part of the Made in Scotland showcase.

For Hector, of course, every single day is one never-ending show, so he took his first theatre experiences in his stride and is probably expecting that, from now on, life will always include people playing the cello to him, blowing bubbles and bounding around in fake forests. At Head in the Clouds, he was as interested in the sparkly shoes of the woman sitting next to us as he was in anything happening on stage. At Poggle, he really enjoyed staring at the other babies. For a brief mad moment, I did consider taking him to stare at the child in Come Look at the Baby but decided that might be a meta-theatre experience too far for both of them.

I fear that in this age, when there is so much anxiety around the behaviour of new theatre-goers in the auditorium, I may have failed to explain the rules to Hector clearly enough. This might explain why, at Head in the Clouds, he tried to eat the props (not a critical comment on the performance) and why at Poggle my failure to explain the concept of the fourth wall meant he kept breaking it with the enthusiasm of the Bolsheviks storming the Winter Palace. At all of these shows, the cast dealt wonderfully with the unpredictability of the young audience, with Hup in particular taking care to ease the babies and toddlers into the performance. It was beautifully designed, too: a wonderful little package for the very young.

Maybe one day, long after I’m gone – like little James Laidlaw, who saw flying pigs and cows – Hector will remember seeing racoons, strange creatures in the forest and a tiny sheepdog chasing floating sheep, and think it was all a dream.